Spiking neural network (SNN) plays an essential role in classification problems. Although there are many models of SNN, Evolving Spiking Neural Network (ESNN) is widely used in many recent research works. Evolutionary algorithms, mainly differential evolution (DE) have been used for enhancing ESNN algorithm. However, many real-world optimization problems include several contradictory objectives. Rather than single optimization, Multi- Objective Optimization (MOO) can be utilized as a set of optimal solutions to solve these problems. In this paper, MOO is used in a hybrid learning of ESNN to determine the optimal pre-synaptic neurons (network structure) and accuracy performance for classification problems simultaneously. Standard data sets from the UCI machine learning are used for evaluating the performance of this multi objective hybrid model. The experimental results have proved that the multi-objective hybrid of Differential Evolution with Evolving Spiking Neural Network (MODE-ESNN) gives better results in terms of accuracy and network structure.